User blog:Lanthoriel/General Theory of Ammunition
Blame for this post entirely belongs to Jalsbury. He planted the seed; it bloomed in my head. The General Theory of Ammunition: The usage of ammunition in G.I. Joe can be encapsulated in the following equation: B = (3Z + 4H + C - L - W)/(E-S) Where Z = # of times slept H = hours online C = ammo consumed from stockpiles (reloads) L = non-streak generating battles, aka losses W = other waste S = streak modifier (average ammo/battle gained) E = efficiency modifier (average ammo/battle used) Specifically, if your average streak length is the following, S = 3: 1/3 6: 2/6 = 1/3 9: 3/9 = 1/3 12: 5/12 15: 7/15 18: 9/18 = 1/2 21: 11/21 24: 13/24 27: 15/27 = 5/9 30: 17/30 During Global Warfare, it is: 3: 1/3 6: 3/6 = 1/2 9: 5/9 12: 7/12 15: 9/15 = 3/5 18: 11/18 21: 13/21 24: 15/24 = 5/8 27: 17/27 30: 19/30 Generally, Z = 1. At maximum efficiency, and assuming Z=1, we arrive at the Special Theory of Ammuntion: B = (3 +4H + C)/(1-S) This tells us the maximum number of battles as a function of hours online, ammunition expended from stocks, and streak efficiency. Derivation: A(produced) = A(used) (Jalsbury-Kirchoff Ammunition Law) Axiomatically, the sum of the ammunition produced must equal the sum of the ammunition used. This is the Jalsbury-Kirchoff Ammunition Law, and is related to the Conservation of Mass. A(free) + A(consumed) + A(awarded) = A(used) (expand left side) Free refers to the ammunition generated at a rate of 1 per 15 minutes. Consumed refers to the amount removed from your inventory as either reloads or restocks. We will hereafter use the variable C to refer to this quantity. If C is negative, the player is increasing their amount of reloads. (3*times slept) + 4*(hours online) + C + A(awarded) = A(used) (Lanthoriel's Sleep Assumption) Assuming a player sleeps for more than 45 minutes, they should have full ammunition when they first play (3 units). If a player sleeps multiple times per day, as long as each time is for more than 45 minutes, they will again have full ammunition from the start. We indicate the number of times a player sleeps by the variable Z. From that point on, for every 15 minutes of play, they gain one unit of ammuniton, or 4 per hour. We will refer to this quantity as H. 3Z + 4H + C + A(awarded) = A(wasted) + (ammunition used per battle)*(number of battles) Ammunition is either wasted or used in battle. We will replace the number of battles with the variable B. 3Z + 4H + C + (streak modifier)*B = (# of non-streak generating losses) + (other waste) + (battle efficiency modifier)*B The number of non-streak generating losses includes any battles over the 3 battle/streak limit. For example, if you lose battle 5, then this value is 2. We will call this amount L. Other waste includes ammunition not picked up under the 45 minute limit, ammunition unused when going to sleep, and other non-categorized wastes, signified by W. The streak modifier under normal conditions is computed as listed above. The constant S refers to the streak modifier. The Battle Efficiency modifier refers to the average amount of ammunition expended per battle. This is found by summing the amount of ammunition used over the average streak length and dividing by the average streak length. At best, it is 1 (no All-Out). At worst, it is 3 (all All-Out). 3Z + 4H + C + SB = L + W + EB Combining terms: 3Z + 4H + C = L + W + (E-S)B Rearranging, solving for B: B = (3Z + 4H + C - L - W)/(E-S) Where Z = # of times slept H = hours online C = ammo consumed from stockpiles (reloads) L = non-streak generating battles, aka losses W = other waste S = streak modifier (average ammo/battle gained) E = efficiency modifier (average ammo/battle used) Of these, C may be positive or negative. S is always fractional, so E-S is always positive. Category:Blog posts